Tree scattering amplitudes of the spin-4/3 fractional superstring I: the untwisted sectors

TL;DR

This paper investigates tree-level scattering amplitudes of the spin-4/3 fractional superstring, demonstrating key properties like decoupling and symmetry, and explores explicit amplitude calculations within a specific algebraic framework.

Contribution

It provides the first explicit calculations of tree scattering amplitudes for the spin-4/3 fractional superstring using a c=5 representation of the fractional superconformal algebra.

Findings

Amplitudes satisfy decoupling and cyclic symmetry at tree level.

Explicit amplitude calculations in a c=5 free boson representation.

Model includes a graviton and is shown to be unitary at tree level.

Abstract

Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by the spin-4/3 fractional superconformal algebra---a parafermionic algebra studied by Zamolodchikov and Fateev involving chiral spin-4/3 currents on the world-sheet in addition to the stress-energy tensor. Examples of tree scattering amplitudes are calculated in an explicit c=5 representation of this fractional superconformal algebra realized in terms of free bosons on the string world-sheet. The target space of this model is three-dimensional flat Minkowski space-time with a level-2 Kac-Moody so(2,1) internal symmetry, and has bosons and fermions in its spectrum. Its closed string version contains a graviton in its spectrum. Tree-level unitarity (i.e., the no-ghost theorem for space-time bosonic physical states) can be shown for this model. Since the critical central charge of the spin-4/3 fractional superstring theory is 10, this c=5 representation cannot be consistent at the string loop level. The existence of a critical fractional superstring containing a four-dimensional space-time remains an open question.